Our strategy for the FT backend is to adaptively find the synthesis plan
that can maximize gate cancellation since the mapping overhead can usually be neglected after applying quantum error correction [1]}.
The pseudocode is shown in Algorithm REF , and we explain it with
Figure REF .
To capture the major gate cancellation opportunities, we scan over all layered blocks and try to select consecutive layer pairs that share the most Pauli operators.
There should be significant operator overlap between consecutive layers since this was considered in our scheduling.
The blocks on the left of Figure REF  are in five layers.
Layer 1, 2, 3, 5 have one block in each and layer 4 has two blocks.
We will pair the layer 3 and 4 together first since they share the same Pauli operators on 6 qubits.
Then the first two layers are paired since they share Pauli operators on only 2 qubits. The last layer is left alone.
